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This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).

The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions.

The authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).

This paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.

Valuation accuracy usually conjures up images of empirical studies of comparisons between sales and valuations and different valuations of the same properties, and a number of references to these studies are included in the paper. However, this paper concentrates on the institutional influences which impact on valuations and their accuracy. The overall aim of this paper is to examine the legal interpretation of valuation inaccuracy in the UK. This might seem a bit parochial in the context of a World Valuation Congress. However, cases in many countries in the Commonwealth form precedents for each other and therefore decisions in, for example, the UK and Australasia, are drawn on by others in reaching decisions. The paper also reaches conclusions which have wider implications for all jurisdictions which have valuation disputes settled in courts, tribunals and any other quasi‐judicial body.

The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics.

This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively.

This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups.

The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric.

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.

It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.

The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system).

Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

Smiths Industries is to supply the head‐up display system for the Sea Harrier. The company will design, develop and make the electronic head‐up display and weapon aiming computer system for the latest version of the HS Harrier which will operate from Royal Navy ships.

Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds.

The authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations.

First the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to.

The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.

In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.

In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H_2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H_2n+1 have constant negative scalar curvature.

In the second part, we present our main results. We show that the Heisenberg group H_2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.

In this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.

The paper aims to quantitatively investigate vacant industrial land valuation accuracy in China, given the importance of the industrial market as an underlying pillar to promote urban growth especially in emerging economies.

In China, the government formulates a Land Benchmark Price (LBP) to serve as a price reference point to sell land rights. To gain an in-depth understanding of the valuation practice by LBP, this paper uses correlation analysis to investigate the varying dynamics between the transaction-based prices and LBP appraisal-based estimates. Furthermore, a margin of error examination investigates the distortion in LBP land appraisals, with an amended LBP presented to improve the accuracy of the current LBP method.

Different influencing factors are identified to impact the actual market transaction prices and the LBP construction, leading to a large discrepancy in industrial land appraisals. A systematic problem is recognised that the construction of the LBP follows urban bid curve theory, whereas the land transaction prices do not, demonstrating that an urgent LBP update is needed to capture the market dynamics for industrial market.

The paper sets out discrepancies in valuation accuracy surrounding the application of the LBP valuation approach in China. This has practical implications for valuers in terms of raising their awareness of the deficiencies in the approach and the pitfalls they need to guard against in their appraisals. It also has implications for developers and investors who rely on valuer appraisals to assess the viability of land purchases; hence, they need to express caution in the appraisal advice sought. Finally, the results demonstrate to the standard setters how they need to modify the LBP equations to better capture market dynamics.

The paper examines valuation accuracy in transitional economies, through valuation differentials between appraised price and the transacted price. The value of the work lies in the analysis of the fundamental differentials between market price and appraised value, which is of importance to investors/developers, practicing valuers, as well as government officials responsible for setting the valuation standards.

The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others.

The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results.

The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions.

The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

The purpose of this paper is to consider “at home ethnography” and “abroad ethnography” not as labels standing for different kinds of fieldwork “out there” but rather as the poles of a continuum identifying the ethnographer’s situated, relative and ever changing epistemic status.

Building on data from a recent fieldwork in an intensive care unit, the author identifies the different epistemic circumstances that originate from the entanglement of the multiple territories of knowledge at stake in any ethnography of complex organizations.

The analysis shows how the participants’ relative access to knowledge and rights to claim it vary according to the circumstances and the unfolding of the interaction. The discussion advances that the ethnographer oscillates between “being abroad” and “being at home” as if he was constantly moving between the two classical positions of ethnographic work: making the familiar strange as it is typical of ethnographies focusing on the “very ‘ordinariness’ of normality” (Ybema et al., 2009, p. 2), and making the strange familiar as it is typical of anthropologists studying exotic communities.

The paper contributes to the still ongoing debate on “at home” organizational ethnography, by addressing the limits of the “insider doctrine” (Merton, 1972) that still pervades contemporary ethnography and proposes cognitive oscillation as the challenging mindset of any ethnographer-in-the-field.